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gecko-dev/browser/devtools/tilt/tilt-math.js

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JavaScript
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/* -*- Mode: javascript; tab-width: 2; indent-tabs-mode: nil; c-basic-offset: 2 -*- */
/* vim: set ts=2 et sw=2 tw=80: */
/* This Source Code Form is subject to the terms of the Mozilla Public
* License, v. 2.0. If a copy of the MPL was not distributed with this
* file, You can obtain one at http://mozilla.org/MPL/2.0/. */
"use strict";
const {Cu} = require("chrome");
let TiltUtils = require("devtools/tilt/tilt-utils");
/**
* Module containing high performance matrix and vector operations for WebGL.
* Inspired by glMatrix, version 0.9.6, (c) 2011 Brandon Jones.
*/
let EPSILON = 0.01;
exports.EPSILON = EPSILON;
const PI_OVER_180 = Math.PI / 180;
const INV_PI_OVER_180 = 180 / Math.PI;
const FIFTEEN_OVER_225 = 15 / 225;
const ONE_OVER_255 = 1 / 255;
/**
* vec3 - 3 Dimensional Vector.
*/
let vec3 = {
/**
* Creates a new instance of a vec3 using the Float32Array type.
* Any array containing at least 3 numeric elements can serve as a vec3.
*
* @param {Array} aVec
* optional, vec3 containing values to initialize with
*
* @return {Array} a new instance of a vec3
*/
create: function V3_create(aVec)
{
let dest = new Float32Array(3);
if (aVec) {
vec3.set(aVec, dest);
} else {
vec3.zero(dest);
}
return dest;
},
/**
* Copies the values of one vec3 to another.
*
* @param {Array} aVec
* vec3 containing values to copy
* @param {Array} aDest
* vec3 receiving copied values
*
* @return {Array} the destination vec3 receiving copied values
*/
set: function V3_set(aVec, aDest)
{
aDest[0] = aVec[0];
aDest[1] = aVec[1];
aDest[2] = aVec[2] || 0;
return aDest;
},
/**
* Sets a vec3 to an zero vector.
*
* @param {Array} aDest
* vec3 to set
*
* @return {Array} the same vector
*/
zero: function V3_zero(aDest)
{
aDest[0] = 0;
aDest[1] = 0;
aDest[2] = 0;
return aDest;
},
/**
* Performs a vector addition.
*
* @param {Array} aVec
* vec3, first operand
* @param {Array} aVec2
* vec3, second operand
* @param {Array} aDest
* optional, vec3 receiving operation result
* if not specified result is written to the first operand
*
* @return {Array} the destination vec3 if specified, first operand otherwise
*/
add: function V3_add(aVec, aVec2, aDest)
{
if (!aDest) {
aDest = aVec;
}
aDest[0] = aVec[0] + aVec2[0];
aDest[1] = aVec[1] + aVec2[1];
aDest[2] = aVec[2] + aVec2[2];
return aDest;
},
/**
* Performs a vector subtraction.
*
* @param {Array} aVec
* vec3, first operand
* @param {Array} aVec2
* vec3, second operand
* @param {Array} aDest
* optional, vec3 receiving operation result
* if not specified result is written to the first operand
*
* @return {Array} the destination vec3 if specified, first operand otherwise
*/
subtract: function V3_subtract(aVec, aVec2, aDest)
{
if (!aDest) {
aDest = aVec;
}
aDest[0] = aVec[0] - aVec2[0];
aDest[1] = aVec[1] - aVec2[1];
aDest[2] = aVec[2] - aVec2[2];
return aDest;
},
/**
* Negates the components of a vec3.
*
* @param {Array} aVec
* vec3 to negate
* @param {Array} aDest
* optional, vec3 receiving operation result
* if not specified result is written to the first operand
*
* @return {Array} the destination vec3 if specified, first operand otherwise
*/
negate: function V3_negate(aVec, aDest)
{
if (!aDest) {
aDest = aVec;
}
aDest[0] = -aVec[0];
aDest[1] = -aVec[1];
aDest[2] = -aVec[2];
return aDest;
},
/**
* Multiplies the components of a vec3 by a scalar value.
*
* @param {Array} aVec
* vec3 to scale
* @param {Number} aVal
* numeric value to scale by
* @param {Array} aDest
* optional, vec3 receiving operation result
* if not specified result is written to the first operand
*
* @return {Array} the destination vec3 if specified, first operand otherwise
*/
scale: function V3_scale(aVec, aVal, aDest)
{
if (!aDest) {
aDest = aVec;
}
aDest[0] = aVec[0] * aVal;
aDest[1] = aVec[1] * aVal;
aDest[2] = aVec[2] * aVal;
return aDest;
},
/**
* Generates a unit vector of the same direction as the provided vec3.
* If vector length is 0, returns [0, 0, 0].
*
* @param {Array} aVec
* vec3 to normalize
* @param {Array} aDest
* optional, vec3 receiving operation result
* if not specified result is written to the first operand
*
* @return {Array} the destination vec3 if specified, first operand otherwise
*/
normalize: function V3_normalize(aVec, aDest)
{
if (!aDest) {
aDest = aVec;
}
let x = aVec[0];
let y = aVec[1];
let z = aVec[2];
let len = Math.sqrt(x * x + y * y + z * z);
if (Math.abs(len) < EPSILON) {
aDest[0] = 0;
aDest[1] = 0;
aDest[2] = 0;
return aDest;
}
len = 1 / len;
aDest[0] = x * len;
aDest[1] = y * len;
aDest[2] = z * len;
return aDest;
},
/**
* Generates the cross product of two vectors.
*
* @param {Array} aVec
* vec3, first operand
* @param {Array} aVec2
* vec3, second operand
* @param {Array} aDest
* optional, vec3 receiving operation result
* if not specified result is written to the first operand
*
* @return {Array} the destination vec3 if specified, first operand otherwise
*/
cross: function V3_cross(aVec, aVec2, aDest)
{
if (!aDest) {
aDest = aVec;
}
let x = aVec[0];
let y = aVec[1];
let z = aVec[2];
let x2 = aVec2[0];
let y2 = aVec2[1];
let z2 = aVec2[2];
aDest[0] = y * z2 - z * y2;
aDest[1] = z * x2 - x * z2;
aDest[2] = x * y2 - y * x2;
return aDest;
},
/**
* Caclulate the dot product of two vectors.
*
* @param {Array} aVec
* vec3, first operand
* @param {Array} aVec2
* vec3, second operand
*
* @return {Array} dot product of the first and second operand
*/
dot: function V3_dot(aVec, aVec2)
{
return aVec[0] * aVec2[0] + aVec[1] * aVec2[1] + aVec[2] * aVec2[2];
},
/**
* Caclulate the length of a vec3.
*
* @param {Array} aVec
* vec3 to calculate length of
*
* @return {Array} length of the vec3
*/
length: function V3_length(aVec)
{
let x = aVec[0];
let y = aVec[1];
let z = aVec[2];
return Math.sqrt(x * x + y * y + z * z);
},
/**
* Generates a unit vector pointing from one vector to another.
*
* @param {Array} aVec
* origin vec3
* @param {Array} aVec2
* vec3 to point to
* @param {Array} aDest
* optional, vec3 receiving operation result
* if not specified result is written to the first operand
*
* @return {Array} the destination vec3 if specified, first operand otherwise
*/
direction: function V3_direction(aVec, aVec2, aDest)
{
if (!aDest) {
aDest = aVec;
}
let x = aVec[0] - aVec2[0];
let y = aVec[1] - aVec2[1];
let z = aVec[2] - aVec2[2];
let len = Math.sqrt(x * x + y * y + z * z);
if (Math.abs(len) < EPSILON) {
aDest[0] = 0;
aDest[1] = 0;
aDest[2] = 0;
return aDest;
}
len = 1 / len;
aDest[0] = x * len;
aDest[1] = y * len;
aDest[2] = z * len;
return aDest;
},
/**
* Performs a linear interpolation between two vec3.
*
* @param {Array} aVec
* first vector
* @param {Array} aVec2
* second vector
* @param {Number} aLerp
* interpolation amount between the two inputs
* @param {Array} aDest
* optional, vec3 receiving operation result
* if not specified result is written to the first operand
*
* @return {Array} the destination vec3 if specified, first operand otherwise
*/
lerp: function V3_lerp(aVec, aVec2, aLerp, aDest)
{
if (!aDest) {
aDest = aVec;
}
aDest[0] = aVec[0] + aLerp * (aVec2[0] - aVec[0]);
aDest[1] = aVec[1] + aLerp * (aVec2[1] - aVec[1]);
aDest[2] = aVec[2] + aLerp * (aVec2[2] - aVec[2]);
return aDest;
},
/**
* Projects a 3D point on a 2D screen plane.
*
* @param {Array} aP
* the [x, y, z] coordinates of the point to project
* @param {Array} aViewport
* the viewport [x, y, width, height] coordinates
* @param {Array} aMvMatrix
* the model view matrix
* @param {Array} aProjMatrix
* the projection matrix
* @param {Array} aDest
* optional parameter, the array to write the values to
*
* @return {Array} the projected coordinates
*/
project: function V3_project(aP, aViewport, aMvMatrix, aProjMatrix, aDest)
{
/*jshint undef: false */
let mvpMatrix = new Float32Array(16);
let coordinates = new Float32Array(4);
// compute the perspective * model view matrix
mat4.multiply(aProjMatrix, aMvMatrix, mvpMatrix);
// now transform that vector into homogenous coordinates
coordinates[0] = aP[0];
coordinates[1] = aP[1];
coordinates[2] = aP[2];
coordinates[3] = 1;
mat4.multiplyVec4(mvpMatrix, coordinates);
// transform the homogenous coordinates into screen space
coordinates[0] /= coordinates[3];
coordinates[0] *= aViewport[2] * 0.5;
coordinates[0] += aViewport[2] * 0.5;
coordinates[1] /= coordinates[3];
coordinates[1] *= -aViewport[3] * 0.5;
coordinates[1] += aViewport[3] * 0.5;
coordinates[2] = 0;
if (!aDest) {
vec3.set(coordinates, aP);
} else {
vec3.set(coordinates, aDest);
}
return coordinates;
},
/**
* Unprojects a 2D point to 3D space.
*
* @param {Array} aP
* the [x, y, z] coordinates of the point to unproject;
* the z value should range between 0 and 1, as clipping plane
* @param {Array} aViewport
* the viewport [x, y, width, height] coordinates
* @param {Array} aMvMatrix
* the model view matrix
* @param {Array} aProjMatrix
* the projection matrix
* @param {Array} aDest
* optional parameter, the array to write the values to
*
* @return {Array} the unprojected coordinates
*/
unproject: function V3_unproject(
aP, aViewport, aMvMatrix, aProjMatrix, aDest)
{
/*jshint undef: false */
let mvpMatrix = new Float32Array(16);
let coordinates = new Float32Array(4);
// compute the inverse of the perspective * model view matrix
mat4.multiply(aProjMatrix, aMvMatrix, mvpMatrix);
mat4.inverse(mvpMatrix);
// transformation of normalized coordinates (-1 to 1)
coordinates[0] = +((aP[0] - aViewport[0]) / aViewport[2] * 2 - 1);
coordinates[1] = -((aP[1] - aViewport[1]) / aViewport[3] * 2 - 1);
coordinates[2] = 2 * aP[2] - 1;
coordinates[3] = 1;
// now transform that vector into space coordinates
mat4.multiplyVec4(mvpMatrix, coordinates);
// invert to normalize x, y, and z values
coordinates[3] = 1 / coordinates[3];
coordinates[0] *= coordinates[3];
coordinates[1] *= coordinates[3];
coordinates[2] *= coordinates[3];
if (!aDest) {
vec3.set(coordinates, aP);
} else {
vec3.set(coordinates, aDest);
}
return coordinates;
},
/**
* Create a ray between two points using the current model view & projection
* matrices. This is useful when creating a ray destined for 3D picking.
*
* @param {Array} aP0
* the [x, y, z] coordinates of the first point
* @param {Array} aP1
* the [x, y, z] coordinates of the second point
* @param {Array} aViewport
* the viewport [x, y, width, height] coordinates
* @param {Array} aMvMatrix
* the model view matrix
* @param {Array} aProjMatrix
* the projection matrix
*
* @return {Object} a ray object containing the direction vector between
* the two unprojected points, the position and the lookAt
*/
createRay: function V3_createRay(aP0, aP1, aViewport, aMvMatrix, aProjMatrix)
{
// unproject the two points
vec3.unproject(aP0, aViewport, aMvMatrix, aProjMatrix, aP0);
vec3.unproject(aP1, aViewport, aMvMatrix, aProjMatrix, aP1);
return {
origin: aP0,
direction: vec3.normalize(vec3.subtract(aP1, aP0))
};
},
/**
* Returns a string representation of a vector.
*
* @param {Array} aVec
* vec3 to represent as a string
*
* @return {String} representation of the vector
*/
str: function V3_str(aVec)
{
return '[' + aVec[0] + ", " + aVec[1] + ", " + aVec[2] + ']';
}
};
exports.vec3 = vec3;
/**
* mat3 - 3x3 Matrix.
*/
let mat3 = {
/**
* Creates a new instance of a mat3 using the Float32Array array type.
* Any array containing at least 9 numeric elements can serve as a mat3.
*
* @param {Array} aMat
* optional, mat3 containing values to initialize with
*
* @return {Array} a new instance of a mat3
*/
create: function M3_create(aMat)
{
let dest = new Float32Array(9);
if (aMat) {
mat3.set(aMat, dest);
} else {
mat3.identity(dest);
}
return dest;
},
/**
* Copies the values of one mat3 to another.
*
* @param {Array} aMat
* mat3 containing values to copy
* @param {Array} aDest
* mat3 receiving copied values
*
* @return {Array} the destination mat3 receiving copied values
*/
set: function M3_set(aMat, aDest)
{
aDest[0] = aMat[0];
aDest[1] = aMat[1];
aDest[2] = aMat[2];
aDest[3] = aMat[3];
aDest[4] = aMat[4];
aDest[5] = aMat[5];
aDest[6] = aMat[6];
aDest[7] = aMat[7];
aDest[8] = aMat[8];
return aDest;
},
/**
* Sets a mat3 to an identity matrix.
*
* @param {Array} aDest
* mat3 to set
*
* @return {Array} the same matrix
*/
identity: function M3_identity(aDest)
{
aDest[0] = 1;
aDest[1] = 0;
aDest[2] = 0;
aDest[3] = 0;
aDest[4] = 1;
aDest[5] = 0;
aDest[6] = 0;
aDest[7] = 0;
aDest[8] = 1;
return aDest;
},
/**
* Transposes a mat3 (flips the values over the diagonal).
*
* @param {Array} aMat
* mat3 to transpose
* @param {Array} aDest
* optional, mat3 receiving operation result
* if not specified result is written to the first operand
*
* @return {Array} the destination mat3 if specified, first operand otherwise
*/
transpose: function M3_transpose(aMat, aDest)
{
if (!aDest || aMat === aDest) {
let a01 = aMat[1];
let a02 = aMat[2];
let a12 = aMat[5];
aMat[1] = aMat[3];
aMat[2] = aMat[6];
aMat[3] = a01;
aMat[5] = aMat[7];
aMat[6] = a02;
aMat[7] = a12;
return aMat;
}
aDest[0] = aMat[0];
aDest[1] = aMat[3];
aDest[2] = aMat[6];
aDest[3] = aMat[1];
aDest[4] = aMat[4];
aDest[5] = aMat[7];
aDest[6] = aMat[2];
aDest[7] = aMat[5];
aDest[8] = aMat[8];
return aDest;
},
/**
* Copies the elements of a mat3 into the upper 3x3 elements of a mat4.
*
* @param {Array} aMat
* mat3 containing values to copy
* @param {Array} aDest
* optional, mat4 receiving operation result
* if not specified result is written to the first operand
*
* @return {Array} the destination mat3 if specified, first operand otherwise
*/
toMat4: function M3_toMat4(aMat, aDest)
{
if (!aDest) {
aDest = new Float32Array(16);
}
aDest[0] = aMat[0];
aDest[1] = aMat[1];
aDest[2] = aMat[2];
aDest[3] = 0;
aDest[4] = aMat[3];
aDest[5] = aMat[4];
aDest[6] = aMat[5];
aDest[7] = 0;
aDest[8] = aMat[6];
aDest[9] = aMat[7];
aDest[10] = aMat[8];
aDest[11] = 0;
aDest[12] = 0;
aDest[13] = 0;
aDest[14] = 0;
aDest[15] = 1;
return aDest;
},
/**
* Returns a string representation of a 3x3 matrix.
*
* @param {Array} aMat
* mat3 to represent as a string
*
* @return {String} representation of the matrix
*/
str: function M3_str(aMat)
{
return "[" + aMat[0] + ", " + aMat[1] + ", " + aMat[2] +
", " + aMat[3] + ", " + aMat[4] + ", " + aMat[5] +
", " + aMat[6] + ", " + aMat[7] + ", " + aMat[8] + "]";
}
};
exports.mat3 = mat3;
/**
* mat4 - 4x4 Matrix.
*/
let mat4 = {
/**
* Creates a new instance of a mat4 using the default Float32Array type.
* Any array containing at least 16 numeric elements can serve as a mat4.
*
* @param {Array} aMat
* optional, mat4 containing values to initialize with
*
* @return {Array} a new instance of a mat4
*/
create: function M4_create(aMat)
{
let dest = new Float32Array(16);
if (aMat) {
mat4.set(aMat, dest);
} else {
mat4.identity(dest);
}
return dest;
},
/**
* Copies the values of one mat4 to another
*
* @param {Array} aMat
* mat4 containing values to copy
* @param {Array} aDest
* mat4 receiving copied values
*
* @return {Array} the destination mat4 receiving copied values
*/
set: function M4_set(aMat, aDest)
{
aDest[0] = aMat[0];
aDest[1] = aMat[1];
aDest[2] = aMat[2];
aDest[3] = aMat[3];
aDest[4] = aMat[4];
aDest[5] = aMat[5];
aDest[6] = aMat[6];
aDest[7] = aMat[7];
aDest[8] = aMat[8];
aDest[9] = aMat[9];
aDest[10] = aMat[10];
aDest[11] = aMat[11];
aDest[12] = aMat[12];
aDest[13] = aMat[13];
aDest[14] = aMat[14];
aDest[15] = aMat[15];
return aDest;
},
/**
* Sets a mat4 to an identity matrix.
*
* @param {Array} aDest
* mat4 to set
*
* @return {Array} the same matrix
*/
identity: function M4_identity(aDest)
{
aDest[0] = 1;
aDest[1] = 0;
aDest[2] = 0;
aDest[3] = 0;
aDest[4] = 0;
aDest[5] = 1;
aDest[6] = 0;
aDest[7] = 0;
aDest[8] = 0;
aDest[9] = 0;
aDest[10] = 1;
aDest[11] = 0;
aDest[12] = 0;
aDest[13] = 0;
aDest[14] = 0;
aDest[15] = 1;
return aDest;
},
/**
* Transposes a mat4 (flips the values over the diagonal).
*
* @param {Array} aMat
* mat4 to transpose
* @param {Array} aDest
* optional, mat4 receiving operation result
* if not specified result is written to the first operand
*
* @return {Array} the destination mat4 if specified, first operand otherwise
*/
transpose: function M4_transpose(aMat, aDest)
{
if (!aDest || aMat === aDest) {
let a01 = aMat[1];
let a02 = aMat[2];
let a03 = aMat[3];
let a12 = aMat[6];
let a13 = aMat[7];
let a23 = aMat[11];
aMat[1] = aMat[4];
aMat[2] = aMat[8];
aMat[3] = aMat[12];
aMat[4] = a01;
aMat[6] = aMat[9];
aMat[7] = aMat[13];
aMat[8] = a02;
aMat[9] = a12;
aMat[11] = aMat[14];
aMat[12] = a03;
aMat[13] = a13;
aMat[14] = a23;
return aMat;
}
aDest[0] = aMat[0];
aDest[1] = aMat[4];
aDest[2] = aMat[8];
aDest[3] = aMat[12];
aDest[4] = aMat[1];
aDest[5] = aMat[5];
aDest[6] = aMat[9];
aDest[7] = aMat[13];
aDest[8] = aMat[2];
aDest[9] = aMat[6];
aDest[10] = aMat[10];
aDest[11] = aMat[14];
aDest[12] = aMat[3];
aDest[13] = aMat[7];
aDest[14] = aMat[11];
aDest[15] = aMat[15];
return aDest;
},
/**
* Calculate the determinant of a mat4.
*
* @param {Array} aMat
* mat4 to calculate determinant of
*
* @return {Number} determinant of the matrix
*/
determinant: function M4_determinant(mat)
{
let a00 = mat[0], a01 = mat[1], a02 = mat[2], a03 = mat[3];
let a10 = mat[4], a11 = mat[5], a12 = mat[6], a13 = mat[7];
let a20 = mat[8], a21 = mat[9], a22 = mat[10], a23 = mat[11];
let a30 = mat[12], a31 = mat[13], a32 = mat[14], a33 = mat[15];
return a30 * a21 * a12 * a03 - a20 * a31 * a12 * a03 -
a30 * a11 * a22 * a03 + a10 * a31 * a22 * a03 +
a20 * a11 * a32 * a03 - a10 * a21 * a32 * a03 -
a30 * a21 * a02 * a13 + a20 * a31 * a02 * a13 +
a30 * a01 * a22 * a13 - a00 * a31 * a22 * a13 -
a20 * a01 * a32 * a13 + a00 * a21 * a32 * a13 +
a30 * a11 * a02 * a23 - a10 * a31 * a02 * a23 -
a30 * a01 * a12 * a23 + a00 * a31 * a12 * a23 +
a10 * a01 * a32 * a23 - a00 * a11 * a32 * a23 -
a20 * a11 * a02 * a33 + a10 * a21 * a02 * a33 +
a20 * a01 * a12 * a33 - a00 * a21 * a12 * a33 -
a10 * a01 * a22 * a33 + a00 * a11 * a22 * a33;
},
/**
* Calculate the inverse of a mat4.
*
* @param {Array} aMat
* mat4 to calculate inverse of
* @param {Array} aDest
* optional, mat4 receiving operation result
* if not specified result is written to the first operand
*
* @return {Array} the destination mat4 if specified, first operand otherwise
*/
inverse: function M4_inverse(aMat, aDest)
{
if (!aDest) {
aDest = aMat;
}
let a00 = aMat[0], a01 = aMat[1], a02 = aMat[2], a03 = aMat[3];
let a10 = aMat[4], a11 = aMat[5], a12 = aMat[6], a13 = aMat[7];
let a20 = aMat[8], a21 = aMat[9], a22 = aMat[10], a23 = aMat[11];
let a30 = aMat[12], a31 = aMat[13], a32 = aMat[14], a33 = aMat[15];
let b00 = a00 * a11 - a01 * a10;
let b01 = a00 * a12 - a02 * a10;
let b02 = a00 * a13 - a03 * a10;
let b03 = a01 * a12 - a02 * a11;
let b04 = a01 * a13 - a03 * a11;
let b05 = a02 * a13 - a03 * a12;
let b06 = a20 * a31 - a21 * a30;
let b07 = a20 * a32 - a22 * a30;
let b08 = a20 * a33 - a23 * a30;
let b09 = a21 * a32 - a22 * a31;
let b10 = a21 * a33 - a23 * a31;
let b11 = a22 * a33 - a23 * a32;
let id = 1 / ((b00 * b11 - b01 * b10 + b02 * b09 +
b03 * b08 - b04 * b07 + b05 * b06) || EPSILON);
aDest[0] = ( a11 * b11 - a12 * b10 + a13 * b09) * id;
aDest[1] = (-a01 * b11 + a02 * b10 - a03 * b09) * id;
aDest[2] = ( a31 * b05 - a32 * b04 + a33 * b03) * id;
aDest[3] = (-a21 * b05 + a22 * b04 - a23 * b03) * id;
aDest[4] = (-a10 * b11 + a12 * b08 - a13 * b07) * id;
aDest[5] = ( a00 * b11 - a02 * b08 + a03 * b07) * id;
aDest[6] = (-a30 * b05 + a32 * b02 - a33 * b01) * id;
aDest[7] = ( a20 * b05 - a22 * b02 + a23 * b01) * id;
aDest[8] = ( a10 * b10 - a11 * b08 + a13 * b06) * id;
aDest[9] = (-a00 * b10 + a01 * b08 - a03 * b06) * id;
aDest[10] = ( a30 * b04 - a31 * b02 + a33 * b00) * id;
aDest[11] = (-a20 * b04 + a21 * b02 - a23 * b00) * id;
aDest[12] = (-a10 * b09 + a11 * b07 - a12 * b06) * id;
aDest[13] = ( a00 * b09 - a01 * b07 + a02 * b06) * id;
aDest[14] = (-a30 * b03 + a31 * b01 - a32 * b00) * id;
aDest[15] = ( a20 * b03 - a21 * b01 + a22 * b00) * id;
return aDest;
},
/**
* Copies the upper 3x3 elements of a mat4 into another mat4.
*
* @param {Array} aMat
* mat4 containing values to copy
* @param {Array} aDest
* optional, mat4 receiving operation result
* if not specified result is written to the first operand
*
* @return {Array} the destination mat4 if specified, first operand otherwise
*/
toRotationMat: function M4_toRotationMat(aMat, aDest)
{
if (!aDest) {
aDest = new Float32Array(16);
}
aDest[0] = aMat[0];
aDest[1] = aMat[1];
aDest[2] = aMat[2];
aDest[3] = aMat[3];
aDest[4] = aMat[4];
aDest[5] = aMat[5];
aDest[6] = aMat[6];
aDest[7] = aMat[7];
aDest[8] = aMat[8];
aDest[9] = aMat[9];
aDest[10] = aMat[10];
aDest[11] = aMat[11];
aDest[12] = 0;
aDest[13] = 0;
aDest[14] = 0;
aDest[15] = 1;
return aDest;
},
/**
* Copies the upper 3x3 elements of a mat4 into a mat3.
*
* @param {Array} aMat
* mat4 containing values to copy
* @param {Array} aDest
* optional, mat3 receiving operation result
* if not specified result is written to the first operand
*
* @return {Array} the destination mat3 if specified, first operand otherwise
*/
toMat3: function M4_toMat3(aMat, aDest)
{
if (!aDest) {
aDest = new Float32Array(9);
}
aDest[0] = aMat[0];
aDest[1] = aMat[1];
aDest[2] = aMat[2];
aDest[3] = aMat[4];
aDest[4] = aMat[5];
aDest[5] = aMat[6];
aDest[6] = aMat[8];
aDest[7] = aMat[9];
aDest[8] = aMat[10];
return aDest;
},
/**
* Calculate the inverse of the upper 3x3 elements of a mat4 and copies
* the result into a mat3. The resulting matrix is useful for calculating
* transformed normals.
*
* @param {Array} aMat
* mat4 containing values to invert and copy
* @param {Array} aDest
* optional, mat3 receiving operation result
* if not specified result is written to the first operand
*
* @return {Array} the destination mat3 if specified, first operand otherwise
*/
toInverseMat3: function M4_toInverseMat3(aMat, aDest)
{
if (!aDest) {
aDest = new Float32Array(9);
}
let a00 = aMat[0], a01 = aMat[1], a02 = aMat[2];
let a10 = aMat[4], a11 = aMat[5], a12 = aMat[6];
let a20 = aMat[8], a21 = aMat[9], a22 = aMat[10];
let b01 = a22 * a11 - a12 * a21;
let b11 = -a22 * a10 + a12 * a20;
let b21 = a21 * a10 - a11 * a20;
let id = 1 / ((a00 * b01 + a01 * b11 + a02 * b21) || EPSILON);
aDest[0] = b01 * id;
aDest[1] = (-a22 * a01 + a02 * a21) * id;
aDest[2] = ( a12 * a01 - a02 * a11) * id;
aDest[3] = b11 * id;
aDest[4] = ( a22 * a00 - a02 * a20) * id;
aDest[5] = (-a12 * a00 + a02 * a10) * id;
aDest[6] = b21 * id;
aDest[7] = (-a21 * a00 + a01 * a20) * id;
aDest[8] = ( a11 * a00 - a01 * a10) * id;
return aDest;
},
/**
* Performs a matrix multiplication.
*
* @param {Array} aMat
* first operand
* @param {Array} aMat2
* second operand
* @param {Array} aDest
* optional, mat4 receiving operation result
* if not specified result is written to the first operand
*
* @return {Array} the destination mat4 if specified, first operand otherwise
*/
multiply: function M4_multiply(aMat, aMat2, aDest)
{
if (!aDest) {
aDest = aMat;
}
let a00 = aMat[0], a01 = aMat[1], a02 = aMat[2], a03 = aMat[3];
let a10 = aMat[4], a11 = aMat[5], a12 = aMat[6], a13 = aMat[7];
let a20 = aMat[8], a21 = aMat[9], a22 = aMat[10], a23 = aMat[11];
let a30 = aMat[12], a31 = aMat[13], a32 = aMat[14], a33 = aMat[15];
let b00 = aMat2[0], b01 = aMat2[1], b02 = aMat2[2], b03 = aMat2[3];
let b10 = aMat2[4], b11 = aMat2[5], b12 = aMat2[6], b13 = aMat2[7];
let b20 = aMat2[8], b21 = aMat2[9], b22 = aMat2[10], b23 = aMat2[11];
let b30 = aMat2[12], b31 = aMat2[13], b32 = aMat2[14], b33 = aMat2[15];
aDest[0] = b00 * a00 + b01 * a10 + b02 * a20 + b03 * a30;
aDest[1] = b00 * a01 + b01 * a11 + b02 * a21 + b03 * a31;
aDest[2] = b00 * a02 + b01 * a12 + b02 * a22 + b03 * a32;
aDest[3] = b00 * a03 + b01 * a13 + b02 * a23 + b03 * a33;
aDest[4] = b10 * a00 + b11 * a10 + b12 * a20 + b13 * a30;
aDest[5] = b10 * a01 + b11 * a11 + b12 * a21 + b13 * a31;
aDest[6] = b10 * a02 + b11 * a12 + b12 * a22 + b13 * a32;
aDest[7] = b10 * a03 + b11 * a13 + b12 * a23 + b13 * a33;
aDest[8] = b20 * a00 + b21 * a10 + b22 * a20 + b23 * a30;
aDest[9] = b20 * a01 + b21 * a11 + b22 * a21 + b23 * a31;
aDest[10] = b20 * a02 + b21 * a12 + b22 * a22 + b23 * a32;
aDest[11] = b20 * a03 + b21 * a13 + b22 * a23 + b23 * a33;
aDest[12] = b30 * a00 + b31 * a10 + b32 * a20 + b33 * a30;
aDest[13] = b30 * a01 + b31 * a11 + b32 * a21 + b33 * a31;
aDest[14] = b30 * a02 + b31 * a12 + b32 * a22 + b33 * a32;
aDest[15] = b30 * a03 + b31 * a13 + b32 * a23 + b33 * a33;
return aDest;
},
/**
* Transforms a vec3 with the given matrix.
* 4th vector component is implicitly 1.
*
* @param {Array} aMat
* mat4 to transform the vector with
* @param {Array} aVec
* vec3 to transform
* @param {Array} aDest
* optional, vec3 receiving operation result
* if not specified result is written to the first operand
*
* @return {Array} the destination vec3 if specified, aVec operand otherwise
*/
multiplyVec3: function M4_multiplyVec3(aMat, aVec, aDest)
{
if (!aDest) {
aDest = aVec;
}
let x = aVec[0];
let y = aVec[1];
let z = aVec[2];
aDest[0] = aMat[0] * x + aMat[4] * y + aMat[8] * z + aMat[12];
aDest[1] = aMat[1] * x + aMat[5] * y + aMat[9] * z + aMat[13];
aDest[2] = aMat[2] * x + aMat[6] * y + aMat[10] * z + aMat[14];
return aDest;
},
/**
* Transforms a vec4 with the given matrix.
*
* @param {Array} aMat
* mat4 to transform the vector with
* @param {Array} aVec
* vec4 to transform
* @param {Array} aDest
* optional, vec4 receiving operation result
* if not specified result is written to the first operand
*
* @return {Array} the destination vec4 if specified, vec4 operand otherwise
*/
multiplyVec4: function M4_multiplyVec4(aMat, aVec, aDest)
{
if (!aDest) {
aDest = aVec;
}
let x = aVec[0];
let y = aVec[1];
let z = aVec[2];
let w = aVec[3];
aDest[0] = aMat[0] * x + aMat[4] * y + aMat[8] * z + aMat[12] * w;
aDest[1] = aMat[1] * x + aMat[5] * y + aMat[9] * z + aMat[13] * w;
aDest[2] = aMat[2] * x + aMat[6] * y + aMat[10] * z + aMat[14] * w;
aDest[3] = aMat[3] * x + aMat[7] * y + aMat[11] * z + aMat[15] * w;
return aDest;
},
/**
* Translates a matrix by the given vector.
*
* @param {Array} aMat
* mat4 to translate
* @param {Array} aVec
* vec3 specifying the translation
* @param {Array} aDest
* optional, mat4 receiving operation result
* if not specified result is written to the first operand
*
* @return {Array} the destination mat4 if specified, first operand otherwise
*/
translate: function M4_translate(aMat, aVec, aDest)
{
let x = aVec[0];
let y = aVec[1];
let z = aVec[2];
if (!aDest || aMat === aDest) {
aMat[12] = aMat[0] * x + aMat[4] * y + aMat[8] * z + aMat[12];
aMat[13] = aMat[1] * x + aMat[5] * y + aMat[9] * z + aMat[13];
aMat[14] = aMat[2] * x + aMat[6] * y + aMat[10] * z + aMat[14];
aMat[15] = aMat[3] * x + aMat[7] * y + aMat[11] * z + aMat[15];
return aMat;
}
let a00 = aMat[0], a01 = aMat[1], a02 = aMat[2], a03 = aMat[3];
let a10 = aMat[4], a11 = aMat[5], a12 = aMat[6], a13 = aMat[7];
let a20 = aMat[8], a21 = aMat[9], a22 = aMat[10], a23 = aMat[11];
aDest[0] = a00;
aDest[1] = a01;
aDest[2] = a02;
aDest[3] = a03;
aDest[4] = a10;
aDest[5] = a11;
aDest[6] = a12;
aDest[7] = a13;
aDest[8] = a20;
aDest[9] = a21;
aDest[10] = a22;
aDest[11] = a23;
aDest[12] = a00 * x + a10 * y + a20 * z + aMat[12];
aDest[13] = a01 * x + a11 * y + a21 * z + aMat[13];
aDest[14] = a02 * x + a12 * y + a22 * z + aMat[14];
aDest[15] = a03 * x + a13 * y + a23 * z + aMat[15];
return aDest;
},
/**
* Scales a matrix by the given vector.
*
* @param {Array} aMat
* mat4 to translate
* @param {Array} aVec
* vec3 specifying the scale on each axis
* @param {Array} aDest
* optional, mat4 receiving operation result
* if not specified result is written to the first operand
*
* @return {Array} the destination mat4 if specified, first operand otherwise
*/
scale: function M4_scale(aMat, aVec, aDest)
{
let x = aVec[0];
let y = aVec[1];
let z = aVec[2];
if (!aDest || aMat === aDest) {
aMat[0] *= x;
aMat[1] *= x;
aMat[2] *= x;
aMat[3] *= x;
aMat[4] *= y;
aMat[5] *= y;
aMat[6] *= y;
aMat[7] *= y;
aMat[8] *= z;
aMat[9] *= z;
aMat[10] *= z;
aMat[11] *= z;
return aMat;
}
aDest[0] = aMat[0] * x;
aDest[1] = aMat[1] * x;
aDest[2] = aMat[2] * x;
aDest[3] = aMat[3] * x;
aDest[4] = aMat[4] * y;
aDest[5] = aMat[5] * y;
aDest[6] = aMat[6] * y;
aDest[7] = aMat[7] * y;
aDest[8] = aMat[8] * z;
aDest[9] = aMat[9] * z;
aDest[10] = aMat[10] * z;
aDest[11] = aMat[11] * z;
aDest[12] = aMat[12];
aDest[13] = aMat[13];
aDest[14] = aMat[14];
aDest[15] = aMat[15];
return aDest;
},
/**
* Rotates a matrix by the given angle around the specified axis.
* If rotating around a primary axis (x, y, z) one of the specialized
* rotation functions should be used instead for performance,
*
* @param {Array} aMat
* mat4 to rotate
* @param {Number} aAngle
* the angle (in radians) to rotate
* @param {Array} aAxis
* vec3 representing the axis to rotate around
* @param {Array} aDest
* optional, mat4 receiving operation result
* if not specified result is written to the first operand
*
* @return {Array} the destination mat4 if specified, first operand otherwise
*/
rotate: function M4_rotate(aMat, aAngle, aAxis, aDest)
{
let x = aAxis[0];
let y = aAxis[1];
let z = aAxis[2];
let len = 1 / (Math.sqrt(x * x + y * y + z * z) || EPSILON);
x *= len;
y *= len;
z *= len;
let s = Math.sin(aAngle);
let c = Math.cos(aAngle);
let t = 1 - c;
let a00 = aMat[0], a01 = aMat[1], a02 = aMat[2], a03 = aMat[3];
let a10 = aMat[4], a11 = aMat[5], a12 = aMat[6], a13 = aMat[7];
let a20 = aMat[8], a21 = aMat[9], a22 = aMat[10], a23 = aMat[11];
let b00 = x * x * t + c, b01 = y * x * t + z * s, b02 = z * x * t - y * s;
let b10 = x * y * t - z * s, b11 = y * y * t + c, b12 = z * y * t + x * s;
let b20 = x * z * t + y * s, b21 = y * z * t - x * s, b22 = z * z * t + c;
if (!aDest) {
aDest = aMat;
} else if (aMat !== aDest) {
aDest[12] = aMat[12];
aDest[13] = aMat[13];
aDest[14] = aMat[14];
aDest[15] = aMat[15];
}
aDest[0] = a00 * b00 + a10 * b01 + a20 * b02;
aDest[1] = a01 * b00 + a11 * b01 + a21 * b02;
aDest[2] = a02 * b00 + a12 * b01 + a22 * b02;
aDest[3] = a03 * b00 + a13 * b01 + a23 * b02;
aDest[4] = a00 * b10 + a10 * b11 + a20 * b12;
aDest[5] = a01 * b10 + a11 * b11 + a21 * b12;
aDest[6] = a02 * b10 + a12 * b11 + a22 * b12;
aDest[7] = a03 * b10 + a13 * b11 + a23 * b12;
aDest[8] = a00 * b20 + a10 * b21 + a20 * b22;
aDest[9] = a01 * b20 + a11 * b21 + a21 * b22;
aDest[10] = a02 * b20 + a12 * b21 + a22 * b22;
aDest[11] = a03 * b20 + a13 * b21 + a23 * b22;
return aDest;
},
/**
* Rotates a matrix by the given angle around the X axis.
*
* @param {Array} aMat
* mat4 to rotate
* @param {Number} aAngle
* the angle (in radians) to rotate
* @param {Array} aDest
* optional, mat4 receiving operation result
* if not specified result is written to the first operand
*
* @return {Array} the destination mat4 if specified, first operand otherwise
*/
rotateX: function M4_rotateX(aMat, aAngle, aDest)
{
let s = Math.sin(aAngle);
let c = Math.cos(aAngle);
let a10 = aMat[4], a11 = aMat[5], a12 = aMat[6], a13 = aMat[7];
let a20 = aMat[8], a21 = aMat[9], a22 = aMat[10], a23 = aMat[11];
if (!aDest) {
aDest = aMat;
} else if (aMat !== aDest) {
aDest[0] = aMat[0];
aDest[1] = aMat[1];
aDest[2] = aMat[2];
aDest[3] = aMat[3];
aDest[12] = aMat[12];
aDest[13] = aMat[13];
aDest[14] = aMat[14];
aDest[15] = aMat[15];
}
aDest[4] = a10 * c + a20 * s;
aDest[5] = a11 * c + a21 * s;
aDest[6] = a12 * c + a22 * s;
aDest[7] = a13 * c + a23 * s;
aDest[8] = a10 * -s + a20 * c;
aDest[9] = a11 * -s + a21 * c;
aDest[10] = a12 * -s + a22 * c;
aDest[11] = a13 * -s + a23 * c;
return aDest;
},
/**
* Rotates a matrix by the given angle around the Y axix.
*
* @param {Array} aMat
* mat4 to rotate
* @param {Number} aAngle
* the angle (in radians) to rotate
* @param {Array} aDest
* optional, mat4 receiving operation result
* if not specified result is written to the first operand
*
* @return {Array} the destination mat4 if specified, first operand otherwise
*/
rotateY: function M4_rotateY(aMat, aAngle, aDest)
{
let s = Math.sin(aAngle);
let c = Math.cos(aAngle);
let a00 = aMat[0], a01 = aMat[1], a02 = aMat[2], a03 = aMat[3];
let a20 = aMat[8], a21 = aMat[9], a22 = aMat[10], a23 = aMat[11];
if (!aDest) {
aDest = aMat;
} else if (aMat !== aDest) {
aDest[4] = aMat[4];
aDest[5] = aMat[5];
aDest[6] = aMat[6];
aDest[7] = aMat[7];
aDest[12] = aMat[12];
aDest[13] = aMat[13];
aDest[14] = aMat[14];
aDest[15] = aMat[15];
}
aDest[0] = a00 * c + a20 * -s;
aDest[1] = a01 * c + a21 * -s;
aDest[2] = a02 * c + a22 * -s;
aDest[3] = a03 * c + a23 * -s;
aDest[8] = a00 * s + a20 * c;
aDest[9] = a01 * s + a21 * c;
aDest[10] = a02 * s + a22 * c;
aDest[11] = a03 * s + a23 * c;
return aDest;
},
/**
* Rotates a matrix by the given angle around the Z axix.
*
* @param {Array} aMat
* mat4 to rotate
* @param {Number} aAngle
* the angle (in radians) to rotate
* @param {Array} aDest
* optional, mat4 receiving operation result
* if not specified result is written to the first operand
*
* @return {Array} the destination mat4 if specified, first operand otherwise
*/
rotateZ: function M4_rotateZ(aMat, aAngle, aDest)
{
let s = Math.sin(aAngle);
let c = Math.cos(aAngle);
let a00 = aMat[0], a01 = aMat[1], a02 = aMat[2], a03 = aMat[3];
let a10 = aMat[4], a11 = aMat[5], a12 = aMat[6], a13 = aMat[7];
if (!aDest) {
aDest = aMat;
} else if (aMat !== aDest) {
aDest[8] = aMat[8];
aDest[9] = aMat[9];
aDest[10] = aMat[10];
aDest[11] = aMat[11];
aDest[12] = aMat[12];
aDest[13] = aMat[13];
aDest[14] = aMat[14];
aDest[15] = aMat[15];
}
aDest[0] = a00 * c + a10 * s;
aDest[1] = a01 * c + a11 * s;
aDest[2] = a02 * c + a12 * s;
aDest[3] = a03 * c + a13 * s;
aDest[4] = a00 * -s + a10 * c;
aDest[5] = a01 * -s + a11 * c;
aDest[6] = a02 * -s + a12 * c;
aDest[7] = a03 * -s + a13 * c;
return aDest;
},
/**
* Generates a frustum matrix with the given bounds.
*
* @param {Number} aLeft
* scalar, left bound of the frustum
* @param {Number} aRight
* scalar, right bound of the frustum
* @param {Number} aBottom
* scalar, bottom bound of the frustum
* @param {Number} aTop
* scalar, top bound of the frustum
* @param {Number} aNear
* scalar, near bound of the frustum
* @param {Number} aFar
* scalar, far bound of the frustum
* @param {Array} aDest
* optional, mat4 frustum matrix will be written into
* if not specified result is written to a new mat4
*
* @return {Array} the destination mat4 if specified, a new mat4 otherwise
*/
frustum: function M4_frustum(
aLeft, aRight, aBottom, aTop, aNear, aFar, aDest)
{
if (!aDest) {
aDest = new Float32Array(16);
}
let rl = (aRight - aLeft);
let tb = (aTop - aBottom);
let fn = (aFar - aNear);
aDest[0] = (aNear * 2) / rl;
aDest[1] = 0;
aDest[2] = 0;
aDest[3] = 0;
aDest[4] = 0;
aDest[5] = (aNear * 2) / tb;
aDest[6] = 0;
aDest[7] = 0;
aDest[8] = (aRight + aLeft) / rl;
aDest[9] = (aTop + aBottom) / tb;
aDest[10] = -(aFar + aNear) / fn;
aDest[11] = -1;
aDest[12] = 0;
aDest[13] = 0;
aDest[14] = -(aFar * aNear * 2) / fn;
aDest[15] = 0;
return aDest;
},
/**
* Generates a perspective projection matrix with the given bounds.
*
* @param {Number} aFovy
* scalar, vertical field of view (degrees)
* @param {Number} aAspect
* scalar, aspect ratio (typically viewport width/height)
* @param {Number} aNear
* scalar, near bound of the frustum
* @param {Number} aFar
* scalar, far bound of the frustum
* @param {Array} aDest
* optional, mat4 frustum matrix will be written into
* if not specified result is written to a new mat4
*
* @return {Array} the destination mat4 if specified, a new mat4 otherwise
*/
perspective: function M4_perspective(
aFovy, aAspect, aNear, aFar, aDest, aFlip)
{
let upper = aNear * Math.tan(aFovy * 0.00872664626); // PI * 180 / 2
let right = upper * aAspect;
let top = upper * (aFlip || 1);
return mat4.frustum(-right, right, -top, top, aNear, aFar, aDest);
},
/**
* Generates a orthogonal projection matrix with the given bounds.
*
* @param {Number} aLeft
* scalar, left bound of the frustum
* @param {Number} aRight
* scalar, right bound of the frustum
* @param {Number} aBottom
* scalar, bottom bound of the frustum
* @param {Number} aTop
* scalar, top bound of the frustum
* @param {Number} aNear
* scalar, near bound of the frustum
* @param {Number} aFar
* scalar, far bound of the frustum
* @param {Array} aDest
* optional, mat4 frustum matrix will be written into
* if not specified result is written to a new mat4
*
* @return {Array} the destination mat4 if specified, a new mat4 otherwise
*/
ortho: function M4_ortho(aLeft, aRight, aBottom, aTop, aNear, aFar, aDest)
{
if (!aDest) {
aDest = new Float32Array(16);
}
let rl = (aRight - aLeft);
let tb = (aTop - aBottom);
let fn = (aFar - aNear);
aDest[0] = 2 / rl;
aDest[1] = 0;
aDest[2] = 0;
aDest[3] = 0;
aDest[4] = 0;
aDest[5] = 2 / tb;
aDest[6] = 0;
aDest[7] = 0;
aDest[8] = 0;
aDest[9] = 0;
aDest[10] = -2 / fn;
aDest[11] = 0;
aDest[12] = -(aLeft + aRight) / rl;
aDest[13] = -(aTop + aBottom) / tb;
aDest[14] = -(aFar + aNear) / fn;
aDest[15] = 1;
return aDest;
},
/**
* Generates a look-at matrix with the given eye position, focal point, and
* up axis.
*
* @param {Array} aEye
* vec3, position of the viewer
* @param {Array} aCenter
* vec3, point the viewer is looking at
* @param {Array} aUp
* vec3 pointing up
* @param {Array} aDest
* optional, mat4 frustum matrix will be written into
* if not specified result is written to a new mat4
*
* @return {Array} the destination mat4 if specified, a new mat4 otherwise
*/
lookAt: function M4_lookAt(aEye, aCenter, aUp, aDest)
{
if (!aDest) {
aDest = new Float32Array(16);
}
let eyex = aEye[0];
let eyey = aEye[1];
let eyez = aEye[2];
let upx = aUp[0];
let upy = aUp[1];
let upz = aUp[2];
let centerx = aCenter[0];
let centery = aCenter[1];
let centerz = aCenter[2];
let z0 = eyex - aCenter[0];
let z1 = eyey - aCenter[1];
let z2 = eyez - aCenter[2];
let len = 1 / (Math.sqrt(z0 * z0 + z1 * z1 + z2 * z2) || EPSILON);
z0 *= len;
z1 *= len;
z2 *= len;
let x0 = upy * z2 - upz * z1;
let x1 = upz * z0 - upx * z2;
let x2 = upx * z1 - upy * z0;
len = 1 / (Math.sqrt(x0 * x0 + x1 * x1 + x2 * x2) || EPSILON);
x0 *= len;
x1 *= len;
x2 *= len;
let y0 = z1 * x2 - z2 * x1;
let y1 = z2 * x0 - z0 * x2;
let y2 = z0 * x1 - z1 * x0;
len = 1 / (Math.sqrt(y0 * y0 + y1 * y1 + y2 * y2) || EPSILON);
y0 *= len;
y1 *= len;
y2 *= len;
aDest[0] = x0;
aDest[1] = y0;
aDest[2] = z0;
aDest[3] = 0;
aDest[4] = x1;
aDest[5] = y1;
aDest[6] = z1;
aDest[7] = 0;
aDest[8] = x2;
aDest[9] = y2;
aDest[10] = z2;
aDest[11] = 0;
aDest[12] = -(x0 * eyex + x1 * eyey + x2 * eyez);
aDest[13] = -(y0 * eyex + y1 * eyey + y2 * eyez);
aDest[14] = -(z0 * eyex + z1 * eyey + z2 * eyez);
aDest[15] = 1;
return aDest;
},
/**
* Returns a string representation of a 4x4 matrix.
*
* @param {Array} aMat
* mat4 to represent as a string
*
* @return {String} representation of the matrix
*/
str: function M4_str(mat)
{
return "[" + mat[0] + ", " + mat[1] + ", " + mat[2] + ", " + mat[3] +
", "+ mat[4] + ", " + mat[5] + ", " + mat[6] + ", " + mat[7] +
", "+ mat[8] + ", " + mat[9] + ", " + mat[10] + ", " + mat[11] +
", "+ mat[12] + ", " + mat[13] + ", " + mat[14] + ", " + mat[15] +
"]";
}
};
exports.mat4 = mat4;
/**
* quat4 - Quaternion.
*/
let quat4 = {
/**
* Creates a new instance of a quat4 using the default Float32Array type.
* Any array containing at least 4 numeric elements can serve as a quat4.
*
* @param {Array} aQuat
* optional, quat4 containing values to initialize with
*
* @return {Array} a new instance of a quat4
*/
create: function Q4_create(aQuat)
{
let dest = new Float32Array(4);
if (aQuat) {
quat4.set(aQuat, dest);
} else {
quat4.identity(dest);
}
return dest;
},
/**
* Copies the values of one quat4 to another.
*
* @param {Array} aQuat
* quat4 containing values to copy
* @param {Array} aDest
* quat4 receiving copied values
*
* @return {Array} the destination quat4 receiving copied values
*/
set: function Q4_set(aQuat, aDest)
{
aDest[0] = aQuat[0];
aDest[1] = aQuat[1];
aDest[2] = aQuat[2];
aDest[3] = aQuat[3];
return aDest;
},
/**
* Sets a quat4 to an identity quaternion.
*
* @param {Array} aDest
* quat4 to set
*
* @return {Array} the same quaternion
*/
identity: function Q4_identity(aDest)
{
aDest[0] = 0;
aDest[1] = 0;
aDest[2] = 0;
aDest[3] = 1;
return aDest;
},
/**
* Calculate the W component of a quat4 from the X, Y, and Z components.
* Assumes that quaternion is 1 unit in length.
* Any existing W component will be ignored.
*
* @param {Array} aQuat
* quat4 to calculate W component of
* @param {Array} aDest
* optional, quat4 receiving calculated values
* if not specified result is written to the first operand
*
* @return {Array} the destination quat if specified, first operand otherwise
*/
calculateW: function Q4_calculateW(aQuat, aDest)
{
if (!aDest) {
aDest = aQuat;
}
let x = aQuat[0];
let y = aQuat[1];
let z = aQuat[2];
aDest[0] = x;
aDest[1] = y;
aDest[2] = z;
aDest[3] = -Math.sqrt(Math.abs(1 - x * x - y * y - z * z));
return aDest;
},
/**
* Calculate the inverse of a quat4.
*
* @param {Array} aQuat
* quat4 to calculate the inverse of
* @param {Array} aDest
* optional, quat4 receiving the inverse values
* if not specified result is written to the first operand
*
* @return {Array} the destination quat if specified, first operand otherwise
*/
inverse: function Q4_inverse(aQuat, aDest)
{
if (!aDest) {
aDest = aQuat;
}
aQuat[0] = -aQuat[0];
aQuat[1] = -aQuat[1];
aQuat[2] = -aQuat[2];
return aQuat;
},
/**
* Generates a unit quaternion of the same direction as the provided quat4.
* If quaternion length is 0, returns [0, 0, 0, 0].
*
* @param {Array} aQuat
* quat4 to normalize
* @param {Array} aDest
* optional, quat4 receiving the operation result
* if not specified result is written to the first operand
*
* @return {Array} the destination quat if specified, first operand otherwise
*/
normalize: function Q4_normalize(aQuat, aDest)
{
if (!aDest) {
aDest = aQuat;
}
let x = aQuat[0];
let y = aQuat[1];
let z = aQuat[2];
let w = aQuat[3];
let len = Math.sqrt(x * x + y * y + z * z + w * w);
if (Math.abs(len) < EPSILON) {
aDest[0] = 0;
aDest[1] = 0;
aDest[2] = 0;
aDest[3] = 0;
return aDest;
}
len = 1 / len;
aDest[0] = x * len;
aDest[1] = y * len;
aDest[2] = z * len;
aDest[3] = w * len;
return aDest;
},
/**
* Calculate the length of a quat4.
*
* @param {Array} aQuat
* quat4 to calculate the length of
*
* @return {Number} length of the quaternion
*/
length: function Q4_length(aQuat)
{
let x = aQuat[0];
let y = aQuat[1];
let z = aQuat[2];
let w = aQuat[3];
return Math.sqrt(x * x + y * y + z * z + w * w);
},
/**
* Performs a quaternion multiplication.
*
* @param {Array} aQuat
* first operand
* @param {Array} aQuat2
* second operand
* @param {Array} aDest
* optional, quat4 receiving the operation result
* if not specified result is written to the first operand
*
* @return {Array} the destination quat if specified, first operand otherwise
*/
multiply: function Q4_multiply(aQuat, aQuat2, aDest)
{
if (!aDest) {
aDest = aQuat;
}
let qax = aQuat[0];
let qay = aQuat[1];
let qaz = aQuat[2];
let qaw = aQuat[3];
let qbx = aQuat2[0];
let qby = aQuat2[1];
let qbz = aQuat2[2];
let qbw = aQuat2[3];
aDest[0] = qax * qbw + qaw * qbx + qay * qbz - qaz * qby;
aDest[1] = qay * qbw + qaw * qby + qaz * qbx - qax * qbz;
aDest[2] = qaz * qbw + qaw * qbz + qax * qby - qay * qbx;
aDest[3] = qaw * qbw - qax * qbx - qay * qby - qaz * qbz;
return aDest;
},
/**
* Transforms a vec3 with the given quaternion.
*
* @param {Array} aQuat
* quat4 to transform the vector with
* @param {Array} aVec
* vec3 to transform
* @param {Array} aDest
* optional, vec3 receiving the operation result
* if not specified result is written to the first operand
*
* @return {Array} the destination vec3 if specified, aVec operand otherwise
*/
multiplyVec3: function Q4_multiplyVec3(aQuat, aVec, aDest)
{
if (!aDest) {
aDest = aVec;
}
let x = aVec[0];
let y = aVec[1];
let z = aVec[2];
let qx = aQuat[0];
let qy = aQuat[1];
let qz = aQuat[2];
let qw = aQuat[3];
let ix = qw * x + qy * z - qz * y;
let iy = qw * y + qz * x - qx * z;
let iz = qw * z + qx * y - qy * x;
let iw = -qx * x - qy * y - qz * z;
aDest[0] = ix * qw + iw * -qx + iy * -qz - iz * -qy;
aDest[1] = iy * qw + iw * -qy + iz * -qx - ix * -qz;
aDest[2] = iz * qw + iw * -qz + ix * -qy - iy * -qx;
return aDest;
},
/**
* Performs a spherical linear interpolation between two quat4.
*
* @param {Array} aQuat
* first quaternion
* @param {Array} aQuat2
* second quaternion
* @param {Number} aSlerp
* interpolation amount between the two inputs
* @param {Array} aDest
* optional, quat4 receiving the operation result
* if not specified result is written to the first operand
*
* @return {Array} the destination quat if specified, first operand otherwise
*/
slerp: function Q4_slerp(aQuat, aQuat2, aSlerp, aDest)
{
if (!aDest) {
aDest = aQuat;
}
let cosHalfTheta = aQuat[0] * aQuat2[0] +
aQuat[1] * aQuat2[1] +
aQuat[2] * aQuat2[2] +
aQuat[3] * aQuat2[3];
if (Math.abs(cosHalfTheta) >= 1) {
aDest[0] = aQuat[0];
aDest[1] = aQuat[1];
aDest[2] = aQuat[2];
aDest[3] = aQuat[3];
return aDest;
}
let halfTheta = Math.acos(cosHalfTheta);
let sinHalfTheta = Math.sqrt(1 - cosHalfTheta * cosHalfTheta);
if (Math.abs(sinHalfTheta) < EPSILON) {
aDest[0] = (aQuat[0] * 0.5 + aQuat2[0] * 0.5);
aDest[1] = (aQuat[1] * 0.5 + aQuat2[1] * 0.5);
aDest[2] = (aQuat[2] * 0.5 + aQuat2[2] * 0.5);
aDest[3] = (aQuat[3] * 0.5 + aQuat2[3] * 0.5);
return aDest;
}
let ratioA = Math.sin((1 - aSlerp) * halfTheta) / sinHalfTheta;
let ratioB = Math.sin(aSlerp * halfTheta) / sinHalfTheta;
aDest[0] = (aQuat[0] * ratioA + aQuat2[0] * ratioB);
aDest[1] = (aQuat[1] * ratioA + aQuat2[1] * ratioB);
aDest[2] = (aQuat[2] * ratioA + aQuat2[2] * ratioB);
aDest[3] = (aQuat[3] * ratioA + aQuat2[3] * ratioB);
return aDest;
},
/**
* Calculates a 3x3 matrix from the given quat4.
*
* @param {Array} aQuat
* quat4 to create matrix from
* @param {Array} aDest
* optional, mat3 receiving the initialization result
* if not specified, a new matrix is created
*
* @return {Array} the destination mat3 if specified, first operand otherwise
*/
toMat3: function Q4_toMat3(aQuat, aDest)
{
if (!aDest) {
aDest = new Float32Array(9);
}
let x = aQuat[0];
let y = aQuat[1];
let z = aQuat[2];
let w = aQuat[3];
let x2 = x + x;
let y2 = y + y;
let z2 = z + z;
let xx = x * x2;
let xy = x * y2;
let xz = x * z2;
let yy = y * y2;
let yz = y * z2;
let zz = z * z2;
let wx = w * x2;
let wy = w * y2;
let wz = w * z2;
aDest[0] = 1 - (yy + zz);
aDest[1] = xy - wz;
aDest[2] = xz + wy;
aDest[3] = xy + wz;
aDest[4] = 1 - (xx + zz);
aDest[5] = yz - wx;
aDest[6] = xz - wy;
aDest[7] = yz + wx;
aDest[8] = 1 - (xx + yy);
return aDest;
},
/**
* Calculates a 4x4 matrix from the given quat4.
*
* @param {Array} aQuat
* quat4 to create matrix from
* @param {Array} aDest
* optional, mat4 receiving the initialization result
* if not specified, a new matrix is created
*
* @return {Array} the destination mat4 if specified, first operand otherwise
*/
toMat4: function Q4_toMat4(aQuat, aDest)
{
if (!aDest) {
aDest = new Float32Array(16);
}
let x = aQuat[0];
let y = aQuat[1];
let z = aQuat[2];
let w = aQuat[3];
let x2 = x + x;
let y2 = y + y;
let z2 = z + z;
let xx = x * x2;
let xy = x * y2;
let xz = x * z2;
let yy = y * y2;
let yz = y * z2;
let zz = z * z2;
let wx = w * x2;
let wy = w * y2;
let wz = w * z2;
aDest[0] = 1 - (yy + zz);
aDest[1] = xy - wz;
aDest[2] = xz + wy;
aDest[3] = 0;
aDest[4] = xy + wz;
aDest[5] = 1 - (xx + zz);
aDest[6] = yz - wx;
aDest[7] = 0;
aDest[8] = xz - wy;
aDest[9] = yz + wx;
aDest[10] = 1 - (xx + yy);
aDest[11] = 0;
aDest[12] = 0;
aDest[13] = 0;
aDest[14] = 0;
aDest[15] = 1;
return aDest;
},
/**
* Creates a rotation quaternion from axis-angle.
* This function expects that the axis is a normalized vector.
*
* @param {Array} aAxis
* an array of elements representing the [x, y, z] axis
* @param {Number} aAngle
* the angle of rotation
* @param {Array} aDest
* optional, quat4 receiving the initialization result
* if not specified, a new quaternion is created
*
* @return {Array} the quaternion as [x, y, z, w]
*/
fromAxis: function Q4_fromAxis(aAxis, aAngle, aDest)
{
if (!aDest) {
aDest = new Float32Array(4);
}
let ang = aAngle * 0.5;
let sin = Math.sin(ang);
let cos = Math.cos(ang);
aDest[0] = aAxis[0] * sin;
aDest[1] = aAxis[1] * sin;
aDest[2] = aAxis[2] * sin;
aDest[3] = cos;
return aDest;
},
/**
* Creates a rotation quaternion from Euler angles.
*
* @param {Number} aYaw
* the yaw angle of rotation
* @param {Number} aPitch
* the pitch angle of rotation
* @param {Number} aRoll
* the roll angle of rotation
* @param {Array} aDest
* optional, quat4 receiving the initialization result
* if not specified, a new quaternion is created
*
* @return {Array} the quaternion as [x, y, z, w]
*/
fromEuler: function Q4_fromEuler(aYaw, aPitch, aRoll, aDest)
{
if (!aDest) {
aDest = new Float32Array(4);
}
let x = aPitch * 0.5;
let y = aYaw * 0.5;
let z = aRoll * 0.5;
let sinr = Math.sin(x);
let sinp = Math.sin(y);
let siny = Math.sin(z);
let cosr = Math.cos(x);
let cosp = Math.cos(y);
let cosy = Math.cos(z);
aDest[0] = sinr * cosp * cosy - cosr * sinp * siny;
aDest[1] = cosr * sinp * cosy + sinr * cosp * siny;
aDest[2] = cosr * cosp * siny - sinr * sinp * cosy;
aDest[3] = cosr * cosp * cosy + sinr * sinp * siny;
return aDest;
},
/**
* Returns a string representation of a quaternion.
*
* @param {Array} aQuat
* quat4 to represent as a string
*
* @return {String} representation of the quaternion
*/
str: function Q4_str(aQuat) {
return "[" + aQuat[0] + ", " +
aQuat[1] + ", " +
aQuat[2] + ", " +
aQuat[3] + "]";
}
};
exports.quat4 = quat4;
/**
* Various algebraic math functions required by the engine.
*/
let TiltMath = {
/**
* Helper function, converts degrees to radians.
*
* @param {Number} aDegrees
* the degrees to be converted to radians
*
* @return {Number} the degrees converted to radians
*/
radians: function TM_radians(aDegrees)
{
return aDegrees * PI_OVER_180;
},
/**
* Helper function, converts radians to degrees.
*
* @param {Number} aRadians
* the radians to be converted to degrees
*
* @return {Number} the radians converted to degrees
*/
degrees: function TM_degrees(aRadians)
{
return aRadians * INV_PI_OVER_180;
},
/**
* Re-maps a number from one range to another.
*
* @param {Number} aValue
* the number to map
* @param {Number} aLow1
* the normal lower bound of the number
* @param {Number} aHigh1
* the normal upper bound of the number
* @param {Number} aLow2
* the new lower bound of the number
* @param {Number} aHigh2
* the new upper bound of the number
*
* @return {Number} the remapped number
*/
map: function TM_map(aValue, aLow1, aHigh1, aLow2, aHigh2)
{
return aLow2 + (aHigh2 - aLow2) * ((aValue - aLow1) / (aHigh1 - aLow1));
},
/**
* Returns if number is power of two.
*
* @param {Number} aNumber
* the number to be verified
*
* @return {Boolean} true if x is power of two
*/
isPowerOfTwo: function TM_isPowerOfTwo(aNumber)
{
return !(aNumber & (aNumber - 1));
},
/**
* Returns the next closest power of two greater than a number.
*
* @param {Number} aNumber
* the number to be converted
*
* @return {Number} the next closest power of two for x
*/
nextPowerOfTwo: function TM_nextPowerOfTwo(aNumber)
{
--aNumber;
for (let i = 1; i < 32; i <<= 1) {
aNumber = aNumber | aNumber >> i;
}
return aNumber + 1;
},
/**
* A convenient way of limiting values to a set boundary.
*
* @param {Number} aValue
* the number to be limited
* @param {Number} aMin
* the minimum allowed value for the number
* @param {Number} aMax
* the maximum allowed value for the number
*/
clamp: function TM_clamp(aValue, aMin, aMax)
{
return Math.max(aMin, Math.min(aMax, aValue));
},
/**
* Convenient way to clamp a value to 0..1
*
* @param {Number} aValue
* the number to be limited
*/
saturate: function TM_saturate(aValue)
{
return Math.max(0, Math.min(1, aValue));
},
/**
* Converts a hex color to rgba.
* If the passed param is invalid, it will be converted to [0, 0, 0, 1];
*
* @param {String} aColor
* color expressed in hex, or using rgb() or rgba()
*
* @return {Array} with 4 color 0..1 components: [red, green, blue, alpha]
*/
hex2rgba: (function()
{
let cache = {};
return function TM_hex2rgba(aColor) {
let hex = aColor.charAt(0) === "#" ? aColor.substring(1) : aColor;
// check the cache to see if this color wasn't converted already
if (cache[hex] !== undefined) {
return cache[hex];
}
// e.g. "f00"
if (hex.length === 3) {
let r = parseInt(hex.substring(0, 1), 16) * FIFTEEN_OVER_225;
let g = parseInt(hex.substring(1, 2), 16) * FIFTEEN_OVER_225;
let b = parseInt(hex.substring(2, 3), 16) * FIFTEEN_OVER_225;
return (cache[hex] = [r, g, b, 1]);
}
// e.g. "f008"
if (hex.length === 4) {
let r = parseInt(hex.substring(0, 1), 16) * FIFTEEN_OVER_225;
let g = parseInt(hex.substring(1, 2), 16) * FIFTEEN_OVER_225;
let b = parseInt(hex.substring(2, 3), 16) * FIFTEEN_OVER_225;
let a = parseInt(hex.substring(3, 4), 16) * FIFTEEN_OVER_225;
return (cache[hex] = [r, g, b, a]);
}
// e.g. "ff0000"
if (hex.length === 6) {
let r = parseInt(hex.substring(0, 2), 16) * ONE_OVER_255;
let g = parseInt(hex.substring(2, 4), 16) * ONE_OVER_255;
let b = parseInt(hex.substring(4, 6), 16) * ONE_OVER_255;
let a = 1;
return (cache[hex] = [r, g, b, a]);
}
// e.g "ff0000aa"
if (hex.length === 8) {
let r = parseInt(hex.substring(0, 2), 16) * ONE_OVER_255;
let g = parseInt(hex.substring(2, 4), 16) * ONE_OVER_255;
let b = parseInt(hex.substring(4, 6), 16) * ONE_OVER_255;
let a = parseInt(hex.substring(6, 8), 16) * ONE_OVER_255;
return (cache[hex] = [r, g, b, a]);
}
// e.g. "rgba(255, 0, 0, 0.5)"
if (hex.match("^rgba")) {
let rgba = hex.substring(5, hex.length - 1).split(",");
rgba[0] *= ONE_OVER_255;
rgba[1] *= ONE_OVER_255;
rgba[2] *= ONE_OVER_255;
// in CSS, the alpha component of rgba() is already in the range 0..1
return (cache[hex] = rgba);
}
// e.g. "rgb(255, 0, 0)"
if (hex.match("^rgb")) {
let rgba = hex.substring(4, hex.length - 1).split(",");
rgba[0] *= ONE_OVER_255;
rgba[1] *= ONE_OVER_255;
rgba[2] *= ONE_OVER_255;
rgba[3] = 1;
return (cache[hex] = rgba);
}
// your argument is invalid
return (cache[hex] = [0, 0, 0, 1]);
};
}())
};
exports.TiltMath = TiltMath;
// bind the owner object to the necessary functions
TiltUtils.bindObjectFunc(vec3);
TiltUtils.bindObjectFunc(mat3);
TiltUtils.bindObjectFunc(mat4);
TiltUtils.bindObjectFunc(quat4);
TiltUtils.bindObjectFunc(TiltMath);
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